A generalization of the finite Fourier transformation and applications
Author:
Ida Roettinger
Journal:
Quart. Appl. Math. 5 (1947), 298-319
MSC:
Primary 42.4X
DOI:
https://doi.org/10.1090/qam/21987
MathSciNet review:
21987
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- Herbert Kapfel Brown, Resolution of temperature problems by the use of finite Fourier transformations, Bull. Amer. Math. Soc. 50 (1944), 376–385. MR 10034, DOI https://doi.org/10.1090/S0002-9904-1944-08149-4
- Herbert Kapfel Brown, The resolution of boundary value problems by means of the finite Fourier transformation: general vibration of a string, J. Appl. Phys. 14 (1943), 609–618. MR 8872
- Herbert Kapfel Brown, General vibration of a hinged beam, J. Appl. Phys. 15 (1944), 410–413. MR 9809
- Ruel V. Churchill, Fourier Series and Boundary Value Problems, McGraw-Hill Book Company, Inc., New York and London, 1941. MR 0003251
- Ruel V. Churchill, Modern Operational Mathematics in Engineering, McGraw-Hill Book Co., Inc., New York, 1944. MR 0010237
Courant-Hilbert, Methoden der mathematischen Physik, Berlin, 1931.
S. R. de Groot, Sur l’intégration de quelques problèmes aux limites régis par l’équation de Fourier dite “de la chaleur” au moyen de la méthode des transformations fonctionnelles simultanées, Nederl. Akad. Wetensch., Proc. 45, 643–649, 820–825 (1942).
G. Doetsch, Integration von Differentialgleichungen vermittels der endlichen Fourier Transformation, Math. Ann. 112, 52–68 (1935).
- Gustav Doetsch, Theorie und Anwendung der Laplace-Transformation, Dover Publication, N. Y., 1943 (German). MR 0009225
Frank-v. Mises, Differentialgleichungen der Physik, 2nd ed. New York, 1943.
S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Warsaw, 1935.
H. Kniess, Lösung von Randwertproblemen bei Systemen gewöhnlicher Differentialgleichungen vermittels der endlichen Fourier Transformation, Math. Zeit. 44, 266–291 (1938).
- Lothar Koschmieder, Die endliche Fouriersche Abbildung und ihr Nutzen bei Aufgaben der Wärmeleitung in Stäben und Platten, Deutsche Math. 5 (1941), 521–545 (German). MR 4357
- Mauro Picone, Appunti d’analisi superiore, Editore Alfredo Rondinella, Napoli, 1940 (Italian). MR 0005359
I. Roettinger, An operational approach to the solution of boundary value problems by generalized Fourier series, Abstract, Bull. Amer. Math. Soc. 51, 67 (1945).
- A. G. Strandhagen, Use of sine transform for non-simply supported beams, Quart. Appl. Math. 1 (1944), 346–348. MR 9409, DOI https://doi.org/10.1090/S0033-569X-1944-09409-X
- C. J. Tranter, On a problem in heat conduction, Philos. Mag. (7) 35 (1944), 102–105. MR 10331
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469
A. Zygmund, Trigonometrical series, Warsaw, 1935.
H. K. Brown, Resolution of temperature problems by use of finite Fourier transformations, Bull. Amer. Math. Soc. 50, 376–385 (1944).
H. K. Brown, The resolution of boundary value problems by means of the finite Fourier transformation: general vibration of a string, J. Appl. Phys. 14, 609–618 (1943).
H. K. Brown, General vibration of a hinged beam, J. Appl. Phys. 15, 410–413 (1944).
R. V. Churchill, Fourier series and boundary value problems, McGraw-Hill, New York, 1941.
R. V. Churchill, Modern operational mathematics in engineering, McGraw-Hill, New York, 1944.
Courant-Hilbert, Methoden der mathematischen Physik, Berlin, 1931.
S. R. de Groot, Sur l’intégration de quelques problèmes aux limites régis par l’équation de Fourier dite “de la chaleur” au moyen de la méthode des transformations fonctionnelles simultanées, Nederl. Akad. Wetensch., Proc. 45, 643–649, 820–825 (1942).
G. Doetsch, Integration von Differentialgleichungen vermittels der endlichen Fourier Transformation, Math. Ann. 112, 52–68 (1935).
G. Doetsch, Theorie und Anwendung der Laplace Transformation, Dover Publications, New York, 1943.
Frank-v. Mises, Differentialgleichungen der Physik, 2nd ed. New York, 1943.
S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Warsaw, 1935.
H. Kniess, Lösung von Randwertproblemen bei Systemen gewöhnlicher Differentialgleichungen vermittels der endlichen Fourier Transformation, Math. Zeit. 44, 266–291 (1938).
L. Koschmieder, Die endliche Fouriersche Abbildung und ihr Nutzen bei Aufgaben der Wärmeleitung in Stäben und Platten, Deutsche Math. 5, 521–545 (1945).
M. Picone, Appunti di analisi superiore, Naples, 1940. pp. 790–793.
I. Roettinger, An operational approach to the solution of boundary value problems by generalized Fourier series, Abstract, Bull. Amer. Math. Soc. 51, 67 (1945).
A. G. Strandhagen, Use of sine transform for non-simply supported beams, Quart. Appl. Math. 1, 346–348 (1944).
C. J. Tranter, On a problem in heat conduction, Philos. Mag. (7) 35, 102–105 (1944).
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, 1940.
A. Zygmund, Trigonometrical series, Warsaw, 1935.
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Article copyright:
© Copyright 1947
American Mathematical Society
